An electronic package with a surface area of $1 m^2$ placed in an orbiting space station is exposed to space. The electronics in this package dissipate all 1 kW of its power to the space through its exposed surface. The exposed surface has an emissivity of 1.0 and an absorptivity of 0.25. Determine the steady state exposed surface temperature of the electronic package (a) if the surface is exposed to a solar flux of $750 W/m^2,$ and (b) if the surface is not exposed to the sun.

A solid plate, with a thickness of 15 cm and a thermal conductivity of $80 W/m \cdot K,$ is being cooled at the upper surface by air. The air temperature is $10^\circ C,$ while the temperatures at the upper and lower surfaces of the plate are 50 and $60^\circ C,$ respectively. Determine the convection heat transfer coefficient of air at the upper surface and discuss whether the value is reasonable or not for force convection of air.

Two surfaces, one highly polished and the other heavily oxidized, are found to be emitting the same amount of energy per unit area. The highly polished surface has an emissivity of 0.1 at $1070^\circ C,$ while the emissivity of the heavily oxidized surface is 0.78. Determine the temperature of the heavily oxidized surface.

A 60-gallon water heater is initially filled with water at $50^\circ F.$ Determine how much energy (in Btu) needs to be transferred to the water to raise its temperature to $120^\circ F.$ Evaluate the water properties at an average water temperature of $85^\circ F.$

A series of experiments were conducted by passing $40^\circ C$ air over a long 25 mm diameter cylinder with an embedded electrical heater. The objective of these experiments was to determine the power per unit length required (Ẇ/L) to maintain the surface temperature of the cylinder at $300^\circ C$ for different air velocities (V). The results of these experiments are given in the following table:

$$\begin{matrix} \text{V(m/s) } & \text{1} & \text{2} & \text{4} & \text{8} & \text{12}\\ \text{W/L(W/m)} & \text{450} & \text{658} & \text{983} & \text{1507} & \text{1963}\\ \end{matrix}$$

(a) Assuming a uniform temperature over the cylinder, negligible radiation between the cylinder surface and surroundings, and steady state conditions, determine the convection heat transfer coefficient (h) for each velocity (V). Plot the results in terms of $h(W/m^2 \cdot K)$ vs. V (m/s). Provide a computer generated graph for the display of your results and tabulate the data used for the graph.(b) Assume that the heat transfer coefficient and velocity can be expressed in the form of $h = CV^n.$ Determine the values of the constants C and n from the results of part (a) by plotting h vs. V on log-log coordinates and choosing a C value that assures a match at V = 1 m/s and then varying n to get the best fit.

A 4-m-diameter spherical tank contains iced water at $0^\circ C.$ The tank is thin-shelled and thus its outer surface temperature may be assumed to be same as the temperature of the iced water inside. Now the tank is placed in a large lake at $20^\circ C.$ The rate at which the ice melts is (a) 0.42 kg/s (b) 0.58 kg/s (c) 0.70 kg/s (d) 0.83 kg/s (e) 0.98kg/s (For lake water, use $k = 0.580 W/m \cdot K, Pr = 9.45, v = 0.1307 \times 10^{-5} m^2/s,\beta = 0.138 \times 10^{-3} K^{-1})$

Does the amount of heat absorbed as 1 kg of saturated liquid water boils at $100^\circ C$ have to be equal to the amount of heat released as 1 kg of saturated water vapor condenses at $100^\circ C?$

An aluminum pan whose thermal conductivity is 237 W/m^2$^\circ{}$C has a flat bottom whose diameter is 20 cm and thickness 0.6 cm. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of 700 W. If the inner surface of the bottom of the pan is 105$^\circ{}$C, determine the temperature of the outer surface of the bottom of the pan.

An aluminum pan whose thermal conductivity is $237 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$ has a flat bottom with diameter 15 cm and thickness 0.4 cm. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of 1400 W. If the inner surface of the bottom of the pan is at $105^\circ C,$ determine the temperature of the outer surface of the bottom of the pan.

Consider a 20-cm thick granite wall with a thermal conductivity of $2.79 W/m \cdot K.$ The temperature of the left surface is held constant at $50^\circ C,$ whereas the right face is exposed to a flow of $22^\circ C$ air with a convection heat transfer coefficient of $15 W/m^2 \cdot K.$ Neglecting heat transfer by radiation, find the right wall surface temperature and the heat flux through the wall.

An aluminum pan whose thermal conductivity is $237 W/m \cdot K$ has a flat bottom with diameter 15 cm and thickness 0.4cm. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of 1400 W. If the inner surface of the bottom of the pan is at $105^\circ C,$ determine the temperature of the outer surface of the bottom of the pan.

Air at $20^\circ C$ with a convection heat transfer coefficient of $25 W/m^2 \cdot K$ blows over a horizontal steel hot plate $(k = 43 W/m \cdot K).$ The surface area of the plate is $0.38 m^2$ with a thickness of 2 cm. The plate surface is maintained at a constant temperature of $T_s = 250^\circ C$ and the plate loses 300 W from its surface by radiation. Calculate the inside plate temperature $(T_i).$

A transistor with a height of 0.4 cm and a diameter of 0.6 cm is mounted on a circuit board. The transistor is cooled by air flowing over it with an average heat transfer coefficient of $30W/m^2 \cdot K.$ If the air temperature is $55^\circ C$ and the transistor case temperature is not to exceed $70^\circ C.$ determine the amount of power this transistor can dissipate safely. Disregard any heat transfer from the transistor base.

Air at $20^\circ C$ with a convection heat transfer coefficient of $20 W/m^2 \cdot K$ blows over a pond. The surface temperature of the pond is at $40^\circ C.$ Determine the heat flux between the surface of the pond and the air.